In the following figure, find the values of x and y.

In △ABC and △ADE,

∠BAC = ∠DAE (Given)

∠BCA = ∠EDA (Given)

AC = AD (Given)

∴ △ABC ≅ △ADE (By ASA axiom)

We know that corresponding parts of congruent triangles are equal.

∴ BC = DE

⇒ x = 2y ……(i)

∴ AB = AE

⇒ 2x + 4 = 3y + 8

Substituting value of x from (i) in above equation we get,

⇒ 2(2y) + 4 = 3y + 8

⇒ 4y + 4 = 3y + 8

⇒ 4y - 3y = 8 - 4

⇒ y = 4.

∴ x = 2y = 2(4) = 8.

Hence, x = 8 and y = 4.